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324 C.C.K. Beh and P.A. Webley/Adsorption Science & Technology Vol. 21 No. 4 2003 the current study), a true multi-bed simulator is needed to model the short-term/dynamic (1–5 cycles) response of the system correctly. The computational demands of a full multi-bed sim- ulator are excessive and would not satisfy the need for future on-line model-based control. Doong and Propsner (1998) have discussed the benefits of multi-bed adsorption process sim- ulators with demonstration on a dual-bed PSA process. Although their model was a single-bed simulator, they attempted to demonstrate the effects of asymmetric operation by adjusting the position of the bed-to-bed valve during the bed-to-bed purge and pressure equalisation steps such that each bed would experience differing purge flows throughout the cycle. Their study showed that operation asymmetry resulted in vastly different performance from that of a sym- metric process simulation. In the field, asymmetric operation is a more common scenario due to the slight variances in piping arrangements, bed packing, and volume and valve positions (especially in the case of the purge valve which is generally designed to flow in a unilateral direction, although in a VSA/PSA process bilateral flow between beds is permitted). The authors also admit that their single-bed simulator with variable bed-to-bed boundary conditions still did not provide a true representation of the dynamics of a multi-bed system. 2. A distributed model is useful when information on distributed variables or variables directly dependent on distributed parameters is needed. In the present study, the main variables of inter- est were purity, flow rate and pressure. Oxygen purity is strongly dependent on the concentra- tion behaviour in the adsorption bed (a distributed variable). If this were the sole variable of interest, then a distributed model would be required. However, product flow rate and pressure are also variables of interest. These are lumped or integrated variables governed largely by flows to and from coupled adsorption tanks with only weak dependence on the spatial infor- mation in the beds. Use of a spatially distributed model therefore is unnecessarily complicated and a lumped parameter model (see c below) is more appropriate. 3. Numerical solution of the coupled conservation equations is sufficiently complex to conceal the physics upon which the equations are based. Tracing which terms in the equations are responsible for the predicted behaviour as a function of time is difficult and extremely tedious. A simpler (perhaps less accurate) model containing the essence of the physics would be more appropriate. (b) Ad hoc arguments followed by construction of an entirely empirical model using correlations between input manipulated variables and responses. Some of the responses of the system (pressure and flow) can be explained using ad hoc arguments. Indeed, these arguments will be used here from time to time. However, at best, these arguments can only provide the direction of the response but not its magnitude nor its time scale. At worst, ad hoc arguments can be completely incorrect. In addition, ad hoc arguments have no predictive power. Whilst black-box type empirical models can be used for prediction (and control purposes), they only apply for situations that exactly match the experimental conditions for which they were derived. They contain no underlying physics and hence provide no ability to predict the effect of perturbations outside the scope of that studied. It is for these reasons that black-box models are only used in process-control structures if reliable mechanistic models are not available, or when the physical model requires impractical computing resource or if mechanistic models are difficult to develop. (c) Solution of a spatially lumped model It is suggested that a lumped model (not spatially distributed) based on a true multi-bed system (including associated gas storage tanks) can serve to explain the direction, magnitude, and timePDF Image | Dynamic Response and Characteristics of an Oxygen Vacuum Swing Adsorption
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